From http://forum.channelnewsasia.com/viewtopic.php?p=3756239
Given cosec A + cot A = 3, evaluate cosec A - cot A and cos A.
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Answer:
cosec A + cot A = 3
(cosec A + cot A) (cosec A - cot A)= 3 (cosec A - cot A)
cosec2 A - cot2 A = 3 (cosec A - cot A)
Since 1 + cot2 A = cosec2 A.....
3 (cosec A - cot A) = 1
cosec A - cot A = 1/3
cosec A + cot A = 3 ----- (1)
cosec A - cot A = 1/3 ----- (2)
Equation (1) + equation (2):
2 cosec A = 10/3
cosec A = 5/3
sin A = 3/5
Equation (1) - equation (2):
2 cot A = 8/3
cot A = 4/3
cos A = sin A * cot A
cos A = 4/5
